I like the idea of this - a self-supporting system. I do wonder how it would go as a roof truss, or even a bridge on a large enough scale. Would you suspend the footpath/road, I wonder, or would it be better as an up-and-over?

I think that Leonardo was actually an alien, otherwise how else could he have come up with all that weird stuff? Helicopters anyone???

Do you really intend to build a shed with it? Talking with authority as one who has successfully boarded out his loft, I think that it will take some extra work to realise this. It's extremely inefficient as it relies on member bending and friction to hold the whole thing together. Have you found that it's awfully flexy too? These are some of the reasons why no one uses this truss form. I'd be hesitant to enter if the shed was more than a couple of meters span and covered with anything heavier than tarpaulin.

As with any truss the timber sizes would have to be appropriately calculated. And though in theory it holds itself together, in practice some sort of connectors would have to be used. It's probably not the most efficient design, or it would likely be used more, though I have seen at least one iteration on youtube. And I have no more room!